[PPT] - Jehoshua (Shuki) Bruck From Screws to Systems The Lineage of BMW PowerPoint Presentation

SLIDE 1

Jehoshua (Shuki) Bruck

SLIDE 2

From Screws to Systems…

SLIDE 3

The Lineage of BMW

SLIDE 4

It happens in biological systems!!!

SLIDE 5

C. Elegans Lineage

total of 959 cells 302 nerve cells 131 cells are destined to die

SLIDE 6

C. Elegans Lineage – Simple Questions

total of 959 cells 302 nerve cells 131 cells are destined to die Dealing with identity: How do cells remember what to do? Dealing with time: How do cells know when? No clock… Dealing with order: How do cells coordinate their actions?

SLIDE 7

Control via Stochastic Chemical Reactions A B C D E F G 1 2 5 4 3

A G E G D F F E D D C B C B A

k k k k k

⎯→ ⎯ + + ⎯→ ⎯ ⎯→ ⎯ + ⎯→ ⎯ + ⎯→ ⎯ +

5 4 3 2 1

SLIDE 8

A G E G D F F E D D C B C B A

k k k k k

⎯→ ⎯ + + ⎯→ ⎯ ⎯→ ⎯ + ⎯→ ⎯ + ⎯→ ⎯ +

5 4 3 2 1

Chemical Reactions Networks 1 2 5 4 3

SLIDE 9

A G E G D F F E D D C B C B A

k k k k k

⎯→ ⎯ + + ⎯→ ⎯ ⎯→ ⎯ + ⎯→ ⎯ + ⎯→ ⎯ +

5 4 3 2 1

Chemical Reactions Networks 1 2 5 4 3

SLIDE 10

A G E G D F F E D D C B C B A

k k k k k

⎯→ ⎯ + + ⎯→ ⎯ ⎯→ ⎯ + ⎯→ ⎯ + ⎯→ ⎯ +

5 4 3 2 1

1 2 5 4 3 Chemical Reactions Networks

SLIDE 11

A G E G D F F E D D C B C B A

k k k k k

⎯→ ⎯ + + ⎯→ ⎯ ⎯→ ⎯ + ⎯→ ⎯ + ⎯→ ⎯ +

5 4 3 2 1

1 2 5 4 3 Chemical Reactions Networks

SLIDE 12

A G E G D F F E D D C B C B A

k k k k k

⎯→ ⎯ + + ⎯→ ⎯ ⎯→ ⎯ + ⎯→ ⎯ + ⎯→ ⎯ +

5 4 3 2 1

1 2 5 4 3 Chemical Reactions Networks

SLIDE 13

A G E G D F F E D D C B C B A

k k k k k

⎯→ ⎯ + + ⎯→ ⎯ ⎯→ ⎯ + ⎯→ ⎯ + ⎯→ ⎯ +

5 4 3 2 1

1 2 5 4 3 Chemical Reactions Networks

SLIDE 14

A G E G D F F E D D C B C B A

k k k k k

⎯→ ⎯ + + ⎯→ ⎯ ⎯→ ⎯ + ⎯→ ⎯ + ⎯→ ⎯ +

5 4 3 2 1

1 2 5 4 3 Chemical Reactions Networks

SLIDE 15

Solving the Puzzle

Mapping and Prediction Principles and Abstractions

A G E G D F F E D D C B C B A

k k k k k

⎯→ ⎯ + + ⎯→ ⎯ ⎯→ ⎯ + ⎯→ ⎯ + ⎯→ ⎯ +

5 4 3 2 1

What are the key players in

in a gene regulatory system?

What are their relevant

interactions?

Success: predictive model
What are the key computational

principles in gene regulations?

A formal language for design

and analysis

Success:

understanding / compression a calculus for Biology

SLIDE 16

Mapping and Prediction

Gillespie, 1976; McAdams and Arkin, 1997 Gibson and Bruck, 2000; Riedel and Bruck 2005 Trajectories Physical chemistry

2

) 1 ( _ _ * * * * * * * * * * *

10 1 , 1 , , ,

9 8 7 6 5 4 3 2 1

t k volume Initial Volume protein no protein protein mRNA Ribosome mRNA Ribosome mRNA Ribosome mRNA Ribosome RNase mRNA RNase mRNA RNase mRNA RNase mRNA Ribosome mRNA Ribosome mRNA DNA RNAP DNA RNAP DNA RNAP DNA RNAP DNA RNAP DNA RNAP

k free free k MAX n k n k k free k free free free free k MAX

pen

n

pen

k n

pen
pen

k closed

+ = ⎯→ ⎯ + + ⎯→ ⎯ ⎯→ ⎯ ⎯→ ⎯ ⎯→ ⎯ + ⎯→ ⎯ + + + ⎯→ ⎯ ⎯→ ⎯ ⎯→ ⎯

+ +

Generating trajectories from stochastic chemical equations We can “see” trajectories and know how compute them faster

SLIDE 17

Descriptive Biology: Is It Sufficient?

SLIDE 18

Early Work on Abstractions

Computing with neural circuits: a connection between logic and neural networks, 1943

Warren McCulloch 1899 - 1969 Walter Pitts 1923 - 1969 Neurophysiologist, MD

Warren McCulloch arrived in early 1942 to the University of Chicago, invited Pitts, who was still homeless, to live with his family. In the evenings McCulloch and Pitts collaborated. Pitts was familiar with the work

f Gottfried Leibniz on computing and they considered the question of whether

the nervous system could be considered a kind of universal computing device as described by Leibniz. This led to their 1943 seminal neural networks paper: A Logical Calculus of Ideas Immanent in Nervous Activity.

Logician, Autodidact

SLIDE 19

Solving the Biology Puzzle

Mapping and Prediction Principles and Abstractions

A G E G D F F E D D C B C B A

k k k k k

⎯→ ⎯ + + ⎯→ ⎯ ⎯→ ⎯ + ⎯→ ⎯ + ⎯→ ⎯ +

5 4 3 2 1

What are the key players in

in a gene regulatory system?

What are their relevant

interactions?

Success: predictive model
What are the key computational

principles in gene regulations?

A formal language for design

and analysis

Success:

understanding / compression a calculus for Biology

SLIDE 20

Key to the Wonderful Progress in Design: Abstractions in Information Systems Reasoning to Calculations to Physics

Circuits Boolean Calculus Reasoning

SLIDE 21

Key to the Progress in Design: Abstractions in Information Systems

Shannon 1916-2001

1938 Boolean Algebra to Electrical Circuits Logic Design 1847 Connected Logic with Algebra Boolean Algebra Logical Calculation

Boole 1815-1864

Logic to Boolean Calculus to Physical Circuits

S D

SLIDE 22

Text to Algebra George Boole, 1854

SLIDE 23

The Algebra (Boolean Calculus)

Boole, DeMorgan, Jevons, Peirce, Schroder (18xx) Postulate System: Huntington (1904)

Algebraic system: set of elements B, two binary operations + and B has at least two elements (0 and 1)

If the following postulates are true

then it is a Boolean Algebra: (i) identity (ii) complement (iii) commutative (vi) distributive

1; a a a a + = ⋅ =

; 1 a = a a = a + ⋅

; a b b a a b b a + = + ⋅ = ⋅

( ) ( ); ( ) a b c a b a c a b c a b a c + ⋅ = + ⋅ + ⋅ + = ⋅ + ⋅

SLIDE 24

Shannon MSc Thesis, 1938 sum carry

Who invented the binary representation

f numbers?

SLIDE 25

Leibniz – Binary System

Gottfried Leibniz 1646-1716

SLIDE 26

Leibniz – Binary System

Gottfried Leibniz 1646-1716

Binary addition algorithm

SLIDE 27

The First Digital Adder George Stibitz, 1904-1995

He worked at Bell Labs in New York. In the fall of 1937 Stibitz used surplus relays, tin can strips, flashlight bulbs, and other common items to construct his "Model K" (K stands for kitchen table). Model K was designed to display the result of the addition of two bits.

SLIDE 28

Key to the Wonderful Progress in Design: Abstractions in Information Systems Reasoning to Calculations to Physics

Circuits Boolean Calculus Reasoning

SLIDE 29

Key Challenge to the Progress in Analysis Abstractions in Information Systems Sensory Forms to Calculations to Reasoning

Reasoning Calculus Sensory Forms

Text
Images
Audio
Numbers
Figures
SW
…

SLIDE 30

Ask a design question: Is it a feature or a bug?

Sensory Forms to Calculations to Reasoning

+ ∧ + ∧ ∨ x y z C S

Biology Engineering

Key Challenge to the Progress in Analysis Abstractions in Information Systems

?? ?? Abstractions

SLIDE 31

Cyclic vs. acyclic (feedback)
Stochastic vs. deterministic

A Feature or a Bug?

??

SLIDE 32

Bio Circuits vs. Combinational Logic Circuits

Joint work with Marc Riedel

Cyclic vs. acyclic (feedback)
Stochastic vs. deterministic

+ ∧ + ∧ ∨

x y z C S

SLIDE 33

Are Cycles a Feature or a Bug?

Hypothesis ????? Cycles might help in

Reducing cost
Increasing performance

SLIDE 34

Circuits With Cycles

a b c

1

f

2

f

3

f

Generally exhibit time-dependent behavior May have unstable/unknown outputs

SLIDE 35

Generally exhibit time-dependent behavior May have unstable/unknown outputs

1 1

? ? ?

0: non-controlling for OR 1: non-controlling for AND

Circuits With Cycles

SLIDE 36

Cyclic Circuits Can be Combinational McCaw’s 1963

Cyclic, 4 AND/OR gates, 5 variables, 2 functions:

OR OR AND AND

SLIDE 37

Cyclic Circuits Can be Combinational McCaw’s 1963

Cyclic, 4 AND/OR gates, 5 variables, 2 functions:

OR OR AND AND

X=0

SLIDE 38

Cyclic Circuits Can be Combinational McCaw’s 1963

Cyclic, 4 AND/OR gates, 5 variables, 2 functions:

OR OR AND AND

X=1

SLIDE 39

Smallest possible equivalent acyclic circuit? 5 AND/OR gates; improvement factor is 4/5

x

1

f b a

OR AND OR OR AND

McCaw’s Circuit (1963)

SLIDE 40

Cyclic Combinational Circuits

Cyclic circuits can be combinational

Short 1961, McCaw 1963, Kautz 1970, Huffman 1971, Rivest 1977

b c b c f1 f2 f3 f4 f5 f6 a a Improvement factor is 2/3 (Rivest 1977) Improvement factor of ½ (Riedel & Bruck 2003)

SLIDE 41

The Role of Cycles in Circuit Design?

Best paper award in 2003 Design Automation Conference

Developed the theory and synthesis techniques for

cyclic combinational circuits Synthesis is based on symbolic analysis

Caltech Cyclify = a software package for the

design of combinational circuits with cycles

Integrated Caltech Cyclify with the Berkeley

design tools

Evaluated benchmark circuits and compared with

current design tools

SLIDE 42

Cycles in Circuits is a Feature!

Cycles help in

Reducing cost
Increasing performance

SLIDE 43

Optimization for Cost (Area)

Cost: Number of NAND2/NOR2 gates

7.47% 1003 1084 s1488 11.66% 758 858 styr 20.54% 673 847 duke2 6.03% 483 514 s510 3.91% 393 409 pma 4.36% 329 344 cse 15.56% 255 302 bw 3.90% 222 231 s386 5.73% 889 943 planet 21.65% 152 194 ex6 10.34% 182 203 5xp1 Improvement Caltech CYCLIFY Berkeley SIS Benchmark

SLIDE 44

Optimization for Performance (Delay) and Fixed Cost

15.22% 39 1.01% 1079 46 1090 s1494 20.93% 34 2.07% 995 43 1016 s1488 10.53% 34 3.50% 716 38 742 duke2 13.89% 31 4.24% 542 36 566 s1 14.29% 24 1.77% 444 28 452 s510 28.57% 20 9.29% 254 28 280 bw 4.35% 22 14.29% 180 23 210 5xp1 14.71% 29 5.42% 558 34 590 in2 17.50% 33 1.00% 593 40 599 in3 17.65% 14 4.66% 327 17 343 t1 21.05% 15 4.57% 167 19 175 p82 Improvement Delay Improvement Area Delay Area benchmark

Caltech CYCLIFY Berkeley SIS

Cost: number of NAND2/NOR2 gates Delay: 1 time unit/gate

SLIDE 45

Bio Circuits vs. Combinational Logic Circuits

Joint work with Cook, Soloveichik and Winfree

+ ∧ + ∧ ∨

x y z C S

Cyclic vs. acyclic (feedback)
Stochastic vs. deterministic

??

SLIDE 46

Computing with Systems

f Chemical Reactions

C B A+

1112 0022 3101 2011 4000

2A D C +

SLIDE 47

The Reachability Question

Given a system of chemical reactions, and an initial state A (1112). Also given is a state B (4000). Starting at A, can the system of chemical reactions reach B?

This question is decidable
The state space is finite!!!
Originally proved by Karp and Miller 1969

in the context of Vector Addition Systems (VAS)

SLIDE 48

Stochastic Chemical Reactions

C B A+

1112 0022 3101

2A D C +

The probability for a reaction to happen is a monotonic function in the number of molecules (#A x #B) or (#C x #D)

SLIDE 49

Stochastic Reachability

Given a system of chemical reactions, and an initial state A. Also given is a state B. Starting at A, is the probability to reach B bigger than 1-small ? Stochastic chemical reactions are Turing universal – with high probability

This question is undecidable

SLIDE 50

Stochastic Behavior is a Feature

Probability enables general (‘precise’) computation in biochemical systems!!

SLIDE 51

Stochastic Behavior is a Feature

Probability enables general (‘precise’) computation in biochemical systems, Proof? Register Machines (Minsky 1967) Register A Register B Programming Unit Infinitely large Idea: Simulate Register Machines with Chemical Reaction Networks Register Machines are universal!! general computing

Marvin Minsky 1927 -

SLIDE 52

Register Machines

Programming Unit Register Machines (Minsky 1967) Register A Register C Inc(A) – increment A and go to the next instruction Dec(A,k) – if A is not 0, decrement A and go to next instruction

therwise, if A is 0, go to instruction k

Register B

SLIDE 53